- #1

Vrbic

- 407

- 18

I have a question, whether is possible to looking for Killing Vectors (KV) in this way (I know about general solution):[itex] [/itex]

From Schwarzschild metric I can see two KV [itex]\frac{\partial}{\partial t} [/itex] and [itex]\frac{\partial}{\partial\phi} [/itex]. Then I see that other trivial KV arent there. Metric in dt and dr is independant on [itex]\theta, \phi [/itex] so I suppose I can "split" metric and looking for KV just in spherical part [itex]d\theta^2+\sin^2{\theta}d\phi^2 [/itex].

Can I suppose transformation this metric to the form: [itex]d\alpha^2+d\beta^2 [/itex] and claim the [itex]\frac{\partial}{\partial\alpha}, \frac{\partial}{\partial\beta} [/itex] are KV?